Question

Suppose samples of six different brands of diet or imitation margarine were analyzed to determine the level of physiologically active polyunsaturated fatty acids (PAPUFA, in percent), resulting in the data shown in the accompanying table. Imperial 14.1 13.6 14.4 14.3 Parkay 12.8 12.5 13.4 13.0 12.3 Blue Bonnet 13.5 13.4 14.1 14.3 Chiffon 13.2 12.7 12.6 14.1 Mazola 16.8 17.2 16.4 17.3 18.0 17.2 18.7 18.4 Fleischmann's 18.1 (a) Test for differences among the true average PAPUFA percentages for the different brands. Use a = 0.05. Calculate the test statistic. (Round your answer to two decimal places.) What can be said about the P-value for this test? OP-value > 0.100 0.050 < P-value < 0.100 0.010 < P-value < 0.050 0.001 < P-value < 0.010 O p-value <0.001 What can you conclude? O Reject Ho. There is not convincing evidence that the mean PAPUFA percentages for the six brands are not all equal. Reject Ho. There is convincing evidence that the mean PAPUFA percentages for the six brands are not all equal. O Fail to reject My. There is convincing evidence that the mean PAPUFA percentages for the six brands are not all equal. O Fail to reject My. There is not convincing evidence that the mean PAPUFA percentages for the six brands are not all equal. (b) Use the T-K procedure to compute 95% simultaneous confidence intervals for all differences between means. (Round your answers to three decimal places.) Imperial and Parkay Imperial and Blue Bonnet Imperial and Chiffon Imperial and Mazola Imperial and Fleischmann's Parkay and Blue Bonnet Parkay and Chiffon Parkay and Mazola Parkay and Fleischmann's Blue Bonnet and Chiffon Blue Bonnet and Mazola Blue Bonnet and Fleischmann's Chiffon and Mazola Chiffon and Fleischmann's Mazola and Fleischmann's

Answer 1

using mintab>stat>basic stat>ANOVA

we have

One-way ANOVA: Imperial, Parkey, Blue Bonnet, Chiffon, Mazola, Fieischmann

Method

Null hypothesis All means are equal
Alternative hypothesis At least one mean is different
Significance level α = 0.05

Equal variances were assumed for the analysis.

Factor Information

Factor Levels Values
Factor 6 Imperial, Parkey, Blue Bonnet, Chiffon, Mazola, Fieischmann

Analysis of Variance

Source DF Adj SS Adj MS F-Value P-Value
Factor 5 107.492 21.4984 74.01 0.000
Error 20 5.809 0.2905
Total 25 113.302

Model Summary

S R-sq R-sq(adj) R-sq(pred)
0.538957 94.87% 93.59% 91.30%

Means

Factor N Mean StDev 95% CI
Imperial 4 14.100 0.356 (13.538, 14.662)
Parkey 5 12.800 0.430 (12.297, 13.303)
Blue Bonnet 4 13.825 0.443 (13.263, 14.387)
Chiffon 4 13.150 0.686 (12.588, 13.712)
Mazola 5 17.140 0.598 (16.637, 17.643)
Fieischmann 4 18.100 0.648 (17.538, 18.662)

Pooled StDev = 0.538957

Tukey Pairwise Comparisons

Grouping Information Using the Tukey Method and 95% Confidence

Factor N Mean Grouping
Fieischmann 4 18.100 A
Mazola 5 17.140 A
Imperial 4 14.100 B
Blue Bonnet 4 13.825 B C
Chiffon 4 13.150 B C
Parkey 5 12.800 C

Means that do not share a letter are significantly different.

Tukey Simultaneous Tests for Differences of Means

Difference SE of Adjusted
Difference of Levels of Means Difference 95% CI T-Value P-Value
Parkey - Imperial -1.300 0.362 (-2.438, -0.162) -3.60 0.019
Blue Bonnet - Imperial -0.275 0.381 (-1.474, 0.924) -0.72 0.977
Chiffon - Imperial -0.950 0.381 (-2.149, 0.249) -2.49 0.173
Mazola - Imperial 3.040 0.362 ( 1.902, 4.178) 8.41 0.000
Fieischmann - Imperial 4.000 0.381 ( 2.801, 5.199) 10.50 0.000
Blue Bonnet - Parkey 1.025 0.362 (-0.113, 2.163) 2.84 0.092
Chiffon - Parkey 0.350 0.362 (-0.788, 1.488) 0.97 0.923
Mazola - Parkey 4.340 0.341 ( 3.267, 5.413) 12.73 0.000
Fieischmann - Parkey 5.300 0.362 ( 4.162, 6.438) 14.66 0.000
Chiffon - Blue Bonnet -0.675 0.381 (-1.874, 0.524) -1.77 0.505
Mazola - Blue Bonnet 3.315 0.362 ( 2.177, 4.453) 9.17 0.000
Fieischmann - Blue Bonnet 4.275 0.381 ( 3.076, 5.474) 11.22 0.000
Mazola - Chiffon 3.990 0.362 ( 2.852, 5.128) 11.04 0.000
Fieischmann - Chiffon 4.950 0.381 ( 3.751, 6.149) 12.99 0.000
Fieischmann - Mazola 0.960 0.362 (-0.178, 2.098) 2.66 0.129

Individual confidence level = 99.49%
a ) the value of F stat = 74.01

p value <0.01

Reject Ho . there is convincing evidence that the mean PAPUFA percentages for six brands are not all equal .

		lower limit	upper limit
Imperial and Parkay		0.162	2.438
Imperial and Blue bonnet		-0.924	1.474
Imperial and chiffon		-0.249	2.149
Imperial and Mazoia		-4.178	-1.902
Imperial and Fleischmann		-5.199	-2.801
Parkey and Blue Bonnet		-2.163	0.113
Parkay and Chiffon		-1.488	0.788
Parkay and Mazola		-5.413	-3.267
Parkay and Fleischmann		-6.438	-4.162
Blue Bonnet and Chiffon		-0.524	1.874
Blue Bonnet and Mazola		-4.453	-3.076
Blue Bonnet and Flieschmann		-5.474	-3.076
Chiffon and Mazola		-5.128	-2.852
Chiffon and Fieschmann		-6.149	-3.751
Mazola and Fieichmann		-2.098	0.178